McCoist has signed Dean Shiels, Francisco Sandaza, Kevin Kyle, Ian Black and Brazilian defender Emilson since his club secured a Scottish Football Association licence.
Brazilian midfielder Andre Moritz ended a trial spell this week after declining the chance to take part in a closed-door game against Hamilton but other hopefuls remain.
McCoist told www.rangersfc.co.uk: “I keep going on about the maths but we do need bodies in. There is no doubt about that, especially with the transfer embargo. We’ve brought four or five lads in to have a look at and to let them take a look at us and at Murray Park and we’d be hopeful that one or two will impress and we can add them to the squad.
“We’re looking everywhere, in defence and in midfield. I keep telling everyone, and I make no apology for it, that it’s a total transformation of the team and the squad in the space of a year.
“We’ve lost 23 or 24 players and will possibly lose more so we need players in all positions.”
McCoist is likely to lose at least one more with Maurice Edu looking for a new club but Carlos Bocanegra and Dorin Goian have both played Rangers’ opening Scottish Football League games.
McCoist, whose team host East Stirlingshire in their first Irn-Bru Third Division home game at Ibrox tomorrow, added: “We don’t want anyone to leave but I have asked them if they are going to, to let me know as soon as possible. That would be a better situation.”